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Is the expansion of the universe uniform? Are there parts which are expanding faster than others? The very fabric of the universe is expanding..but is it expanding at a constant rate? If it is not then how do we measure the distance of the stars as the light would get unevely streched in each width of space due to non-uniform expansion under Doppler 's effect?

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The expansion of the universe is certainly not uniform. For example, you are not expanding - your local density is much higher than the critical density. Neither is the Earth expanding.

The universe is also not expanding at a constant rate. The rate of expansion is measured by the Hubble constant, which isn't really a constant - it varies with time.

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The cosmological expansion is very highly isotropic (to about one part in a hundred thousand!), based on observations of the spectrum of cosmic microwave background (CMB) photons reaching Earth from completely different parts of the universe.

The standard cosmological model assumes that on the largest scales the universe is homogeneous as well as isotropic.

Addendum: If downvoters don’t believe this former cosmologist, perhaps they will believe Wikipedia:

Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us, as predicted by a universal expansion. Using the redshift of their electromagnetic spectra to determine the distance and speed of remote objects in space, he showed that all objects are moving away from us, and that their speed is proportional to their distance, a feature of metric expansion. Further studies have since shown the expansion to be highly isotropic and homogeneous.

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  • $\begingroup$ So do we have to correct for the ongoing expansion while the light is travelling to the Earth while applying Doppler's effect to calculate distance to the stars? $\endgroup$ – Schwarz Kugelblitz Jul 7 at 4:28
  • $\begingroup$ Yes, that’s right. $\endgroup$ – G. Smith Jul 7 at 4:28
  • $\begingroup$ How is that exactly done? $\endgroup$ – Schwarz Kugelblitz Jul 7 at 4:28
  • $\begingroup$ Is is same to assume that the universe is isotopic without affecting other parameters? $\endgroup$ – Schwarz Kugelblitz Jul 7 at 4:29
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    $\begingroup$ @Allure You’re wrong. If it were expanding anisotropically, the CMB redshift be different in different directions. $\endgroup$ – G. Smith Jul 7 at 16:15
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Of course G. Smith's answer is right, but let me add a few things:

  1. inside galaxies, space is not expanding, since gravity dominates over dark energy

  2. now between galaxy clusters, space is expanding, dark energy is dominant, but the rate of expansion here is not as fast as in the voids of superclusters

  3. On the large scale, the universe expands uniformly, but as you go from the space between galaxy clusters to viods between superclusters, the rate of expansion is increasing

Please see here:

https://physics.stackexchange.com/a/482814/132371

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  • $\begingroup$ Ok ..but there is no hard boundary to a galaxy right...we can only be sure of a general area in space where gravity and dark energy switch dominance? $\endgroup$ – Schwarz Kugelblitz Jul 9 at 18:25
  • $\begingroup$ @HerambPodar yes you are correct $\endgroup$ – Árpád Szendrei Jul 9 at 18:25

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